Another:Coprime to sum of permutation's terms

[Leroy Quet]

I just submitted:

>%S A000001 1,2,3,4,6,5,8,9,10,7,12,11,14,13,16,15,18,19,22,17,20
>%N A000001 a(1)=1. a(2)=2. a(n) = lowest positive integer not occurring 
>earlier in the sequence such that GCD(a(n-2),a(n-1)+a(n)) = 1.
>%C A000001 Sequence may be a permutation of the positive integers.
>%e A000001 Among the positive integers not occurring among the first 6 
>terms of the sequence, 8 is the lowest m such that GCD(a(5),a(6)+m) = 
>GCD(6,5+m) = 1.
>Had we used 7 for m instead, we would have had GCD(6,5+7) = 6. So a(7) = 8.
>%O A000001 1
>%K A000001 ,more,nonn,

As I also asked in another recent seq.fan post:
Is this a permutation of the positive integers?

thanks,
Leroy Quet